A shock wave ("blast") has mechanical force. If this wave of compressed air hits a human body while traveling at high speed, it can do massive damage in much the same way as a vehicle moving at high speed. Of course, the shock wave is made of compressed air which has a lot more give and a lot less mass than your average car. So, it's rather like being hit by a very light car with pillows or bubble wrap on the front end. But, it's also moving a lot faster than most cars.

A blast that detonates underwater can be more deadly than a blast in air, but only to people who are in that water. The person who is in the water near an explosive device when it goes off will be hit by a blast wave made of compressed water rather than compressed air. However, an explosive that detonates in water is less dangerous to people standing nearby, but out of the water. The person standing close enough to be killed by a bomb if it were sitting on the ground could survive the same blast if the bomb were placed in a bucket of water. The water absorbs much of the kinetic energy of the blast.

I should also point out that grenades kill and injure people with their shrapnel, almost exclusively. This is why the explosive core of the grenade is wrapped in bits of metal that are cut into small squares or rectangles. If you are standing next to a grenade when it goes off, and by some extraordinary stroke of luck all the bits of shrapnel happened to miss you, you will probably survive with only some eardrum damage. Stun grenades, or "flash bang" grenades, operate on this principle. They produce a large blast but almost no shrapnel. The noise and brightness of the flash are very disorienting, and the shock wave can actually knock a person down, but the chances of being killed by one, even at close proximity, are very slim.